The purpose of this book is to provide an elementary yet systematic description of the
Bogoliubov-de Gennes (BdG) equations their unique symmetry properties and their relation to
Green's function theory. Specifically it introduces readers to the supercell technique for the
solutions of the BdG equations as well as other related techniques for more rapidly solving
the equations in practical applications.The BdG equations are derived from a microscopic model
Hamiltonian with an effective pairing interaction and fully capture the local electronic
structure through self-consistent solutions via exact diagonalization. This approach has been
successfully generalized to study many aspects of conventional and unconventional
superconductors with inhomogeneities - including defects disorder or the presence of a
magnetic field - and becomes an even more attractive choice when the first-principles
information of a typical superconductor is incorporated via the construction of a low-energy
tight-binding model. Further the lattice BdG approach is essential when theoretical results
for local electronic states around such defects are compared with the scanning tunneling
microscopy measurements. Altogether these lectures provide a timely primer for graduate
students and non-specialist researchers while also offering a useful reference guide for
experts in the field.
